Subgroups — C₃×C₅×#2326 #14275360

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#385	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2326	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₃×C₅×#124	C₄	1	8	yes	complemented
15	C₃×C₄×C₅×Q₈	—	2	4	no	—
16	C₃×C₄×C₅×D₄	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	4	yes	—
31	C₃×#2326	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
35	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#390	C₂×C₃	1	1	yes	characteristic
37	C₅×#388	C₂×C₃	1	4	yes	complemented
38	C₅×#385	C₂×C₃	1	4	yes	complemented
39	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	—	4	4	no	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	4	4	no	—
62	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
63	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
65	C₃×C₄²×C₅	—	2	4	no	—
66	C₃×C₄²×C₅	—	2	2	no	—
67	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
68	C₃×C₄²×C₅	D₄	1	4	yes	—
69	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
70	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
72	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×#390	C₂×C₅	1	1	yes	characteristic
74	C₃×#388	C₂×C₅	1	4	yes	complemented
75	C₃×#385	C₂×C₅	1	4	yes	complemented
76	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
81	C₅×#124	C₃×C₄	1	8	yes	complemented
82	C₄×C₅×Q₈	—	2	4	no	—
83	C₄×C₅×D₄	—	2	4	no	—
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
91	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
93	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
95	C₅×#95	C₂²×C₃	1	2	yes	—
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	C₅×#95	C₂²×C₃	1	4	yes	—
98	#2326	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	4	no	—
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
104	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
105	C₃×C₅×Q₈	—	2	8	no	—
106	C₃×C₅×D₄	—	2	8	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	4	8	no	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	#41	1	2	yes	—
128	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
129	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
130	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
131	C₃×#124	C₄×C₅	1	8	yes	complemented
132	C₃×C₄×Q₈	—	2	4	no	—
133	C₃×C₄×D₄	—	2	4	no	—
134	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
141	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
145	C₃×#95	C₂²×C₅	1	2	yes	—
146	C₃×#95	C₂²×C₅	1	2	yes	—
147	C₃×#95	C₂²×C₅	1	4	yes	—
148	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
149	C₂×C₅×Q₈	—	2	2	no	—
150	C₂×C₅×Q₈	—	2	2	no	—
151	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
155	C₂²×C₄×C₅	—	2	4	no	—
156	C₂²×C₄×C₅	—	4	4	no	—
157	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
158	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	4	4	no	—
169	C₅×C₂²⋊C₄	—	2	4	no	—
170	C₅×C₂²⋊C₄	—	4	4	no	—
171	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
172	C₄²×C₅	—	2	4	no	—
173	C₄²×C₅	—	2	2	no	—
174	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
175	C₄²×C₅	C₃×D₄	1	4	yes	—
176	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
177	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
178	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
179	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
180	#390	C₂×C₃×C₅	1	1	yes	characteristic
181	#388	C₂×C₃×C₅	1	4	yes	complemented
182	#385	C₂×C₃×C₅	1	4	yes	complemented
183	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
184	#376	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	C₂²×C₃×C₅	—	2	4	no	—
186	C₂²×C₃×C₅	—	2	8	no	—
187	C₂²×C₃×C₅	—	4	2	no	—
188	C₂²×C₃×C₅	—	4	2	no	—
189	C₂²×C₃×C₅	—	4	4	no	—
190	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
191	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
193	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
194	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
195	C₃×C₄×C₅	—	2	4	no	—
196	C₃×C₄×C₅	—	2	4	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
203	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
204	C₂×C₃×Q₈	—	2	2	no	—
205	C₂×C₃×Q₈	—	2	2	no	—
206	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
207	C₂×C₃×D₄	—	2	2	no	—
208	C₂×C₃×D₄	—	2	2	no	—
209	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
210	C₂²×C₃×C₄	—	2	4	no	—
211	C₂²×C₃×C₄	—	4	4	no	—
212	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
214	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
215	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
216	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₃×C₄⋊C₄	—	2	2	no	—
221	C₃×C₄⋊C₄	—	2	4	no	—
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄⋊C₄	—	4	4	no	—
224	C₃×C₂²⋊C₄	—	2	4	no	—
225	C₃×C₂²⋊C₄	—	4	4	no	—
226	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
227	C₃×C₄²	—	2	4	no	—
228	C₃×C₄²	—	2	2	no	—
229	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
230	C₃×C₄²	C₅×D₄	1	4	yes	—
231	C₂³×C₅	—	2	2	no	—
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	2	4	no	—
234	C₂³×C₅	—	2	4	no	—
235	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
236	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
237	C₅×Q₈	—	2	8	no	—
238	C₅×D₄	—	2	8	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	4	8	no	—
253	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
254	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
255	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
256	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
257	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
259	C₂×C₄×C₅	C₃×#41	1	2	yes	—
260	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
261	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
262	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
263	#124	C₃×C₄×C₅	1	8	yes	complemented
264	C₄×Q₈	—	2	4	no	—
265	C₄×D₄	—	2	4	no	—
266	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
269	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
270	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
272	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
273	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
274	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
275	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
276	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
277	#95	C₂²×C₃×C₅	1	2	yes	—
278	#95	C₂²×C₃×C₅	1	2	yes	—
279	#95	C₂²×C₃×C₅	1	4	yes	—
280	C₂×C₃×C₅	—	4	4	no	—
281	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂×C₃×C₅	#520	1	2	yes	—
283	C₂×C₃×C₅	#535	1	1	yes	characteristic
284	C₂×C₃×C₅	#536	1	1	yes	characteristic
285	C₂×C₃×C₅	#542	1	2	yes	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	2	no	—
288	C₂³×C₃	—	2	4	no	—
289	C₂³×C₃	—	2	4	no	—
290	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
291	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
292	C₃×Q₈	—	2	8	no	—
293	C₃×D₄	—	2	8	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	4	no	—
305	C₂×C₃×C₄	—	2	4	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	4	8	no	—
308	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
309	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
310	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
311	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
312	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
313	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
314	C₂×C₃×C₄	C₅×#41	1	2	yes	—
315	C₂²×C₅	—	2	4	no	—
316	C₂²×C₅	—	2	8	no	—
317	C₂²×C₅	—	4	2	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	4	4	no	—
320	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
321	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
323	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
324	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
325	C₄×C₅	—	2	4	no	—
326	C₄×C₅	—	2	4	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	4	2	no	—
332	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
333	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
343	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
344	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
345	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
346	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
347	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
348	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
349	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	16	yes	complemented
357	C₄²	—	2	4	no	—
358	C₄²	—	2	2	no	—
359	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
360	C₄²	C₃×C₅×D₄	1	4	yes	—
361	C₃×C₅	#2326	1	1	yes	characteristic, direct product factor, Hall
362	C₂²×C₃	—	2	4	no	—
363	C₂²×C₃	—	2	8	no	—
364	C₂²×C₃	—	4	2	no	—
365	C₂²×C₃	—	4	2	no	—
366	C₂²×C₃	—	4	4	no	—
367	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
368	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
369	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
370	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
371	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
372	C₃×C₄	—	2	4	no	—
373	C₃×C₄	—	2	4	no	—
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	4	2	no	—
377	C₃×C₄	—	4	2	no	—
378	C₃×C₄	—	4	2	no	—
379	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
380	C₂×C₅	—	4	4	no	—
381	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
382	C₂×C₅	C₃×#520	1	2	yes	—
383	C₂×C₅	C₃×#535	1	1	yes	characteristic
384	C₂×C₅	C₃×#536	1	1	yes	characteristic
385	C₂×C₅	C₃×#542	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
391	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
392	Q₈	—	2	8	no	—
393	D₄	—	2	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
409	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
410	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
411	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
412	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
413	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
414	C₂×C₄	C₃×C₅×#41	1	2	yes	—
415	C₂×C₃	—	4	4	no	—
416	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
417	C₂×C₃	C₅×#520	1	2	yes	—
418	C₂×C₃	C₅×#535	1	1	yes	characteristic
419	C₂×C₃	C₅×#536	1	1	yes	characteristic
420	C₂×C₃	C₅×#542	1	2	yes	—
421	C₅	C₃×#2326	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	2	4	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
428	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
429	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
430	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
431	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
432	C₄	—	2	4	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
440	C₃	C₅×#2326	1	1	yes	characteristic, direct product factor, Sylow
441	C₂	—	4	4	no	—
442	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
443	C₂	C₃×C₅×#520	1	2	yes	—
444	C₂	C₃×C₅×#535	1	1	yes	characteristic
445	C₂	C₃×C₅×#536	1	1	yes	characteristic
446	C₂	C₃×C₅×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₃×C₅×#385	C₂	semidirect
8. C₃×C₅×#384	C₂	semidirect
9. C₃×C₅×#376	C₂	semidirect
10. C₅×#2326	C₃	direct (N × H)
14. C₃×C₅×#124	C₄	semidirect
31. C₃×#2326	C₅	direct (N × H)
33. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
35. C₅×#391	C₂×C₃	semidirect
37. C₅×#388	C₂×C₃	semidirect
38. C₅×#385	C₂×C₃	semidirect
39. C₅×#384	C₂×C₃	semidirect
40. C₅×#376	C₂×C₃	semidirect
44. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
64. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
67. C₃×C₄²×C₅	C₂×C₄	semidirect
70. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
72. C₃×#391	C₂×C₅	semidirect
74. C₃×#388	C₂×C₅	semidirect
75. C₃×#385	C₂×C₅	semidirect
76. C₃×#384	C₂×C₅	semidirect
77. C₃×#376	C₂×C₅	semidirect
81. C₅×#124	C₃×C₄	semidirect
98. #2326	C₃×C₅	direct (N × H)
131. C₃×#124	C₄×C₅	semidirect
151. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
171. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
174. C₄²×C₅	C₂×C₃×C₄	semidirect
177. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
179. #391	C₂×C₃×C₅	semidirect
181. #388	C₂×C₃×C₅	semidirect
182. #385	C₂×C₃×C₅	semidirect
183. #384	C₂×C₃×C₅	semidirect
184. #376	C₂×C₃×C₅	semidirect
206. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
226. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
229. C₃×C₄²	C₂×C₄×C₅	semidirect
263. #124	C₃×C₄×C₅	semidirect
336. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
356. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
359. C₄²	C₂×C₃×C₄×C₅	semidirect
361. C₃×C₅	#2326	direct (N × H)
421. C₅	C₃×#2326	direct (N × H)
440. C₃	C₅×#2326	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#124	2
C₂×C₃×C₄×C₅×Q₈	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#391	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#385	2
C₃×C₅×#384	2
C₃×C₅×#376	2
C₅×#2326	3
C₃×#2326	5

Subgroups — C3×C5×#2326 #14275360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2326 #14275360